Method for image reconstruction of moving radionuclide source distribution

ABSTRACT

A method for image reconstruction of moving radionuclide distributions. Its particular embodiment is for single photon emission computed tomography (SPECT) imaging of awake animals, though its techniques are general enough to be applied to other moving radionuclide distributions as well. The invention eliminates motion and blurring artifacts for image reconstructions of moving source distributions. This opens new avenues in the area of small animal brain imaging with radiotracers, which can now be performed without the perturbing influences of anesthesia or physical restraint on the biological system.

The United States of America may have certain rights to this inventionunder Management and Operating Contract DE-AC05-060R23177 from theUnited States Department of Energy.

FIELD OF THE INVENTION

The present invention relates to radionuclide image reconstructiontechniques and more particularly to such techniques that are useful inthe imaging of moving radionuclide sources.

BACKGROUND OF THE INVENTION

For human and animal single photon emission computed tomography (SPECT)imaging, anesthesia and physical restraints may be used to reduce oreliminate motion, however these methods may directly influence thepharmacokinetics of the relevant biological system or cause stress thatmay indirectly affect radiotracer uptake and retention. These effectsare pronounced in brain scanning. Imaging unanesthetized, unrestrainedsmall animals can provide unique capabilities for biomedical research byeliminating the impact of anesthetic on the animal brain function andreducing the stress to the animal, thus opening new possibilities in thearea of brain studies.

Conventional image reconstruction for emission computed tomographyassumes that the source activity distribution and the human, animal orobject being imaged are static. This assumption is not necessarily truefor human imaging, where there may be some head or body motion, forimaging unanesthetized animals where the animal may be in motion, or forimaging plants where there may be motion due to the wind or mechanicaldisturbances. Image reconstruction without motion compensation resultsin blurred and degraded images, which affects the interpretation andquantitative measurement of radiotracer distribution. Smaller regions ofradionuclide accumulation are more difficult to discern. For biologicalimaging this degradation due to motion influences the measurement ofphysiological parameters from the radiotracer biodistribution. It wouldbe of great benefit to provide a system for imaging such moving objects,humans and animals, without these blurring artifacts.

OBJECT OF THE INVENTION

It is therefore an object of the present invention to provide a methodfor imaging moving objects such as humans and animals, without theoccurrence of blurring artifacts.

SUMMARY OF THE INVENTION

The present invention provides a method for image reconstruction ofmoving radionuclide distributions. Its particular embodiment is forsingle photon emission computed tomography (SPECT) imaging of awakeanimals, though its techniques are general enough to be applied to othermoving radionuclide distributions as well. The invention eliminatesmotion and blurring artifacts for image reconstructions of moving sourcedistributions. This opens new avenues in the area of small animal brainimaging with radiotracers, which can now be performed without theperturbing influences of anesthesia or physical restraint on thebiological system.

DESCRIPTION OF THE DRAWINGS

FIGS. 1( a-c) are one-dimensional projections of a reconstructed imagevolume of: (a) a static phantom data set; (b) a moving phantom data setwith motion corrections; and (c) a moving phantom data set withoutmotion corrections.

FIG. 2 is a schematic representation of the geometry of the systemdescribed herein.

FIG. 3 is a schematic representation of the calibration block used inaccordance with the present invention.

FIG. 4 is a block diagram of the operation of the present invention.

DETAILED DESCRIPTION

U.S. Pat. No. 7,209,579 issued Apr. 24, 2007 which is incorporatedherein by reference in its entirety, describes a functional imagingsystem for use in the imaging of unrestrained and non-anesthetized smallanimals or other subjects and a method for acquiring such images andfurther registering them with anatomical X-ray images previously orsubsequently acquired. The apparatus comprises a combination of an IRlaser profilometry system and gamma, PET and/or SPECT, imaging system,all mounted on a rotating gantry, that permits simultaneous acquisitionof positional and orientational information and functional images of anunrestrained subject that are registered, i.e. integrated, using imageprocessing software to produce a functional image of the subject withoutthe use of restraints or anesthesia. The functional image thus obtainedcan be registered with a previously or subsequently obtained X-ray CTimage of the subject. That system permitted functional imaging of asubject in an unrestrained/non-anesthetized condition thereby reducingthe stress on the subject and eliminating any potential interferencewith the functional testing that such stress might induce. The methoddescribed herein extends and refines the method and the application ofthe apparatus described in U.S. Pat. No. 7,209,579.

In small animal imaging in accordance with the techniques described inU.S. Pat. No. 7,209,579, image motion is recorded at a rate of 10-15frames per second, for scan times typically 20-30 minutes. TomographicSPECT images cannot be obtained for these individual time frames becausegamma cameras do not rotate quickly enough to obtain data over 360degrees. For PET, image reconstructions of individual time frames couldbe made, rotated and translated in 3-D, and then summed, though theindividual frames would be extremely noisy due to the count poor natureof the input data. Summing of a large number of such sub-images toobtain a resultant image has not previously been performed.

The motion correction equation described herein corrects forthree-dimensional source motion, rather than just correcting for linearmotion of 2-D SPECT projection data, as is sometimes performed forpatient motion in SPECT cardiac imaging.

The image reconstruction equation described herein uses all recordedevents simultaneously in a unified image reconstruction program thatcorrects for motion affecting all ray paths.

The image reconstruction method of the present invention in its smallanimal SPECT brain imaging embodiment uses data from a small animalSPECT scanner whose construction is similar to the device described inU.S. Pat. No. 7,209,579 with certain critical modifications fortomographic SPECT and PET imaging. Firstly, three retroreflectors (notdepicted) are glued to the head of the small animal depicted in FIGS. 2,4-5 and 6-7 of U.S. Pat. No. 7,209,579. A real-time optical trackingsystem with three cameras provides continuous time stamped pose data ofthe awake animal head during the SPECT scan, typically 10-15 times/sec.The pose data that is written to a disk file consists of six geometricparameters: three displacements and three angles, with respect to theinitial head position. The scintillation events recorded by the gammacamera also are time stamped and written to a file in list-mode.Time-stamped information on the position of the rotating gantry, towhich the gamma camera is attached, is written to a third file. Thetracking system, gantry and gamma camera clocks are synchronized.

A calibration scan is performed prior to imaging of a moving object todetermine the transformation between the gamma camera reference frameand the tracking reference frame. The specially designed calibrationphantom 10 (see FIG. 3), consisting of three optical markers and threeradioactive sources, is scanned in a stationary configuration. Thisphantom is shown in FIG. 3 and described more fully below. The relativepositions of the optical markers and the radioactive sources are knownfrom the phantom design. The data are reconstructed and coordinates ofsources in the reconstruction coordinate frame are obtained. A computerprogram then calculates coordinate transformation between tracking andgamma camera coordinate systems.

Information from the three input files is used in an iterative list-modemaximum likelihood expectation maximization algorithm described below.During image reconstruction the image volume of the activitydistribution is transformed from the gamma camera reference frame to thetracking reference frame. A transformation for motion correction isimplemented and then the image volume is transformed back to the gammacamera reference frame, in which ray tracing for the iterativereconstruction algorithm is performed.

The foregoing process is outlined generally in FIG. 4 wherein it isshown that list-mode single photon data, gamma camera motion data andpose data are integrated with the calibration scan data using thealgorithm described below to obtain a reconstructed image of the liveunanesthetized animal or subject.

In detail, image is accomplished as follows. Data from all threesubsystem files are read in. Projection data are created byhistogramming the list-mode data. First, timing intervals during whichthe gantry is stationary are identified. Next the pose records arecompared, and if all six parameters from two successive pose recordsvary by no more than preset threshold values, the gamma event is addedto a 2-D projection image. A new projection image is formed whenever thegamma camera moves or if the pose difference threshold values areexceeded. Note that a threshold value of zero is equivalent toperforming no histogramming.

During the iteration steps, the detector is stationary and thereconstruction volume is transformed according to the tracking andgantry location information. A standard iterative maximum likelihoodexpectation maximization (MLEM) algorithm is utilized, with additionalnormalization for different acquisition times per projection. The MLEMalgorithm used in accordance with the present invention is as follows:

$s_{j}^{n + 1} = {\frac{s_{j}^{n}}{\sum\limits_{i}A_{i\; j}}{\sum\limits_{i}{{A_{i\; j}\left\lbrack \frac{p_{i,{meas}}}{\sum\limits_{k}{A_{i\; k}s_{k}^{n}}} \right\rbrack}.}}}$

In application, the calibration phantom is imaged with and withoutmotion, and reconstructed with and without motion compensation. Thecalibration phantom 10 is depicted in FIG. 3 wherein three opticalreflectors 12A, 12B and 12C and three Co⁵⁷ point sources 14A, 14B and14C are provided. FIG. 2 depicts a schematic view of the geometry of theapparatus utilized in accordance with the present invention. A moredetailed view of a suitable such apparatus is depicted in the abovereferenced Figures of U.S. Pat. No. 7,209,579. As shown in FIG. 2, theapparatus 20 comprises a gantry 22 rotating in the direction shown byarrows 24. The positions of gamma cameras 26A and 26B (gamma referenceframe GRF) are associated with the SPECT reconstruction volume 28 andthe angle of rotation 30. The coordinate system of the GRF is denoted byarrows X, Y, and Z. The positions of gamma cameras 26A and 26B aremeasured in the GRF. The tracking reference frame (TRF) is defined asthe coordinate system of the optical cameras 32A, 32B, and 32C. Thecoordinate system of the TRF is denoted by arrows X^(I),Y^(I), andZ^(I).

Image reconstruction is performed in the reference frame of the gammacamera (GRF) and so the position of a point in the source object oranimal must be computed as a function of time in this reference frame.From direct measurements with the motion tracking system the objectmotion is only known as a function of time in the tracking referenceframe (TRF), however. The 3-D point position in the GRF can be computedfrom the motion in the TRF by the vector equationx(GRF, t)=R _(TG) [R _(pose)(t)R ⁻¹ _(pose)(t ₀){R ⁻¹ _(TG) [x(GRF, t₀)−t _(TG) ]−t _(pose)(t ₀)}+t _(pose)(t)]+t _(TG)wherein:

-   x(GRF, t) is the 3-D position of a source object point in the gamma    reference frame as a function of time t;-   x(GRF, t₀) is the 3-D position of a source object point in the gamma    reference frame at a starting time t₀;-   R_(TG) and t_(TG) are the 3-D rotation matrix and the 3-component    translation vector describing the transformation from the tracking    reference frame to the gamma reference frame; (That is, the    coordinates of a point in the gamma reference frame are given by the    equation x(GRF)=R_(TG)x(TRF)+t_(TG). The values of R_(TG) and t_(TG)    are determined from calibration experiments with a dual modality    phantom having retroreflectors and radioactive sources.)-   R⁻¹ _(TG) is the matrix inverse of R_(TG), so that the coordinates    of a point in the tracking reference frame can be computed from the    coordinates in the gamma reference frame by the equation    x(TRF)=R ⁻¹ _(TG) [x(GRF)−t _(TG)];-   R_(pose)(t) are t_(pose)(t) are the time-dependent 3-D rotation    matrix and the 3-component translation vector describing the motion    of a point in the tracking reference frame from a reference position    to a position at time t. (The motion tracking system provides this    information, which in raw form is given by three rotation parameters    (roll, pitch, yaw) and 3 orthogonal translation parameters.)-   R⁻¹ _(pose)(t) is the inverse of the matrix R_(pose)(t);-   R_(pose)(t₀) and t_(pose)(t₀) are the pose rotation matrix and pose    translation vector at a time t₀ to be used for the object position    for image reconstruction. Time t₀ is usually taken to be the    position at the start of the scan.)

Conceptually the above equation does the following:

1) transforms the coordinates of a source object point in the gammareference frame at time t₀ to its coordinates in the tracking referenceframe (using R⁻¹ _(TG) and t_(TG));

2) transforms the point position in the tracking reference frame to itsposition at the reference tracking position (using R⁻¹ _(pose)(t₀) andt_(pose)(t₀));

3) applies the measured motion transformation in the tracking referenceframe (using R_(pose)(t) and t_(pose)(t)); and

4) transforms the coordinates from the tracking reference frame back tothe gamma reference frame (using R_(TG) and t_(TG)).

Raytracing for forward and backprojection in iterative imagereconstruction uses the motion-corrected source voxel positions as givenby the above equation, for example in implementations of the maximumlikelihood expectation maximization method or the ordered subsetsexpectation maximization method.

The spatial resolution full width half maximum (FWHM) of the movingpoint sources with motion correction is only about 0.1 mm worse thanthat of the point sources imaged without motion. Reconstructions of anawake animal scan with and without motion compensation were performed.Visual comparison of the slices through reconstructed head volumesreveals significant improvement of image quality when motion correctionsare implemented. Table 1 below demonstrates Full width at half maximumsof profiles taken through each gamma source.

TABLE 1 Static Corrected FWHM FWHM (mm) (mm) Point 1 1.93 2.07 Point 2 2.03 2.11 Point 3 1.95 2.01

FIGS. 1( a-c) are one-dimensional projections of a reconstructed imagevolume of: (a) a static phantom data set: (b) a moving phantom data setwith motion corrections: and (c) a moving phantom data set withoutmotion corrections.

There has thus been described a method for image reconstruction ofmoving radionuclide distributions. The invention eliminates motion andblurring artifacts for image reconstructions of moving sourcedistributions. More specifically, the method comprises: A) imaging athree dimensional calibration phantom including at least threereflective markers and at least three gamma sources with and withoutmotion in a tracking system comprising: I) an imaging volume for limitedconfinement of the subject; II) a rotating gantry about said imagingvolume; III) at least three cameras that scan said three dimensionalphantom and form an image generated by light reflected from thereflective markers as the cameras scan the subject, to spatially locatethe phantom within the imaging volume mounted on the rotating gantry; atleast two SPECT and/or PET imaging devices also mounted on the gantry inpositions to permit said light sources and said cameras to view saidimaging volume and spatially locate and map the phantom while said SPECTand/or PET imaging devices functionally image the phantom; and IV) imageprocessing hardware and software that receive electronic signals fromsaid tracking system and said cameras and generate a combined andregistered profile and a functional image of the phantom; and B)repeating the process of step A while a living unanesthetized subjectlabeled with at least three optical reflectors and having previouslybeen injected with a radiopharmaceutical is located in the imagingvolume; and C) obtaining a functional image of the unanesthetizedsubject through the application of suitable 3-D positioning equationsand an iterative list-mode maximum likelihood expectation maximizationalgorithm that is part of the software.

As will be apparent to the skilled artisan, a number of variations andmodifications can be made to the system described above withoutdeparting from the spirit and scope of the present invention. All suchmodifications and changes are clearly contemplated as being within thescope of the invention as defined by the appended claims.

1. A method for image reconstruction of moving radionuclidedistributions in an unanesthetized living subject comprising: A) imaginga three dimensional phantom including at least three reflective markersand at least three gamma sources with and without motion in a trackingsystem comprising: I) an imaging volume for limited confinement of thephantom; II) a rotating gantry about said imaging volume; III) at leastthree optical cameras that scan said three dimensional phantom, toobtain a tracking reference frame, and form an image generated by lightreflected from the reflective markers as the optical cameras scan saidphantom, to spatially locate the phantom within the imaging volumemounted on the rotating gantry; IV) at least two SPECT and/or PETimaging devices mounted on the gantry, to obtain a gamma referenceframe, in positions to permit said optical cameras to view said imagingvolume and spatially locate and map the phantom while said SPECT and/orPET imaging devices functionally image the phantom; and V) imageprocessing hardware and software that receive electronic signals fromsaid tracking system and said SPECT and/or PET imaging devices andgenerate a combined and registered profile and a functional image of thephantom; and B) repeating the process of step A while the livingunanesthetized subject labeled with at least three optical reflectorsand having previously been injected with a radiopharmaceutical islocated in the imaging volume in place of the phantom; and C) obtaininga functional image of the unanesthetized living subject through theapplication of a vector equation and an iterative list-mode maximumlikelihood expectation maximization algorithm that is part of thesoftware; wherein said vector equation isx(GRF,t)=R _(TG) [R _(pose)(t)R ⁻¹ _(pose)(t ₀){R ⁻¹ _(TG) [x(GRF,t ₀)−t_(TG) ]−t _(pose)(t ₀)}+t _(pose)(t)]+t _(TG) and; x(GRF, t) is a 3-Dposition of a source object point in the gamma reference frame as afunction of time t; x(GRF, t₀) is a 3-D position of a source objectpoint in the gamma reference frame at a starting time t₀; R_(TG) andt_(TG) are a 3-D rotation matrix and a 3-component translation vectordescribing the transformation from the tracking reference frame to thegamma reference frame; R⁻¹ _(TG) is the matrix inverse of R_(TG);R_(pose)(t) and t_(pose)(t) are a time-dependent 3-D rotation matrix anda 3-component translation vector describing a motion of a point in thetracking reference frame from a reference position to a position at timet; R_(pose)(t₀) and t_(pose)(t₀)are a pose rotation matrix and posetranslation vector at a time t₀ to be used for the object position forimage reconstruction; and R⁻¹ _(pose)(t₀) is the inverse of the matrixR_(pose)(t₀).
 2. A method for image reconstruction of movingradionuclide distributions in an unanesthetized living subjectcomprising: A) attaching at least three retroreflectors to a smallanimal to be imaged; B) using a real-time optical tracking systemincluding at least three optical cameras attached to a rotating gantryobtaining continuous time stamped pose data of the unanesthetized livingsubject to obtain a tracking reference frame; C) simultaneouslyperforming a SPECT scan using at least two gamma cameras attached to thegantry to obtain time stamped gamma list mode data; D) simultaneouslyobtaining time-stamped position information on the position of therotating gantry; E) synchronizing the tracking system, gantry and timestamped gamma list mode data; F) performing a calibration scan totransform from the tracking reference frame to a gamma reference frame;and G) reconstructing the image in the gamma reference frame through theapplication of a vector equation and an iterative list-mode maximumlikelihood expectation maximization algorithm that is part of thesoftware, wherein said vector equation isx(GRF,t)=R _(TG) [R _(pose)(t)R ⁻¹ _(pose)(t ₀){R ⁻¹ _(TG) [x(GRF,t ₀)−t_(TG) ]−t _(pose)(t ₀)}+t _(pose)(t)]+t _(TG) and; x(GRF, t) is a 3-Dposition of a source object point in the gamma reference frame as afunction of time t; x(GRF, t₀) is a 3-D position of a source objectpoint in the gamma reference frame at a starting time t₀; R_(TG) andt_(TG) are the 3-D rotation matrix and a 3-component translation vectordescribing the transformation from the tracking reference frame to thegamma reference frame; R⁻¹ _(TG) is the matrix inverse of R_(TG);R_(pose)(t) and t_(pose)(t) are a time-dependent 3-D rotation matrix anda 3-component translation vector describing a motion of a point in thetracking reference frame from a reference position to a position at timet; R_(pose)(t₀) and t_(pose)(t₀) are a pose rotation matrix and posetranslation vector at a time t₀ to be used for the source objectposition for image reconstruction; and R⁻¹ _(pose)(t₀) is the inverse ofthe matrix R_(pose)(t₀).